I've got two fake shoulders. One is essentially a replacement (hemiarthroplasty). The other is a real fucking mess and required the glenoid to be re-constructed and a new socket to be made grafting bone and taking connective tissue with it (latarjet procedure).
The rehab is long and painful for both, and six months is likely an under-estimate until you get something *approximating* the normal use of your arm back. Seriously, you fight for every half-angle of degree of motion in every direction. I can remember the day that I was able to put my hand in my back pocket -- the friction held it there to stretch one of the heads of the deltoid and it felt so good that I was reminded of the Arnold "in the gym I am cumming all the time" thing.
The short answer is, overhead pressing is not a necessity. This is the blessing and the curse of the shoulder -- the anatomy is so complicated that there's about a million ways to damage it, but there's an equal number of ways to train it. You've got cables, machines, incline bench pressing (bar and dumbbell), bodybuilding approach that separate the heads of the delt into primary movers... getting or keeping strong shoulders will not be a problem.
I don't know the status of your shoulder or the cause of the impairment, but my two cents (that may be worth ignoring)... your focus from now on is shoulder health. Everything else comes second. Flexibility and the strength of the rotator cuff -- to protect the actual structure of the joint -- is what you need to be asking about. Get a PT and pay out of pocket if you have to... it'll be the best money you ever spend.